Isomonodromic deformations of linear differential equations [1]} have been studied intensively and admit many applications both in mathematics and physics. The recent paper [2]} revealed a connection between isomonodromic deformation and the Liouville conformal field theory that the tau function of the sixth Painlevé equation \(\mathrm {P_{VI}}\)  is a Fourier transform of the Virasoro conformal block with central charge \(c=1\) . Later, the tau functions of other Painlevé equations \(\mathrm {P_V}\) , \(\mathrm {P_{IV}}\) , \(\mathrm {P_{III}}\) , \(\mathrm {P_{II}}\)  were also recognized as Fourier transforms of irregular conformal blocks [3]}, [4]}, [5]}, [6]}. Furthermore, the tau functions of isomonodromic deformation of particular Fuchsian systems of rank \(N\)  was constructed by semi-degenerate conformal blocks of \(W_N\) -algebra with central charge \(c=N-1\)  [7]}.
